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A329938
Beatty sequence for sinh x, where csch x + sech x = 1 .
3
1, 3, 5, 7, 9, 11, 13, 15, 16, 18, 20, 22, 24, 26, 28, 30, 32, 33, 35, 37, 39, 41, 43, 45, 47, 48, 50, 52, 54, 56, 58, 60, 62, 64, 65, 67, 69, 71, 73, 75, 77, 79, 80, 82, 84, 86, 88, 90, 92, 94, 96, 97, 99, 101, 103, 105, 107, 109, 111, 112, 114, 116, 118
OFFSET
1,2
COMMENTS
Let x be the solution of csch x + sech x = 1. Then (floor(n*sinh x)) and (floor(n*cosh x)) are a pair of Beatty sequences; i.e., every positive integer is in exactly one of the sequences. See the Guide to related sequences at A329825.
FORMULA
a(n) = floor(n*sinh x), where x = 1.390148... is the constant in A329937; a(n) first differs from A329831(n) at n = 77.
MATHEMATICA
Solve[1/Sinh[x] + 1/Cosh[x] == 1, x]
r = ArcSech[1/8 (4 - 4 Sqrt[2] - 9 Sqrt[5 + 4 Sqrt[2]] + (5 + 4 Sqrt[2])^(3/2))];
u = N[r, 250]
v = RealDigits[u][[1]];
Table[Floor[n*Sinh[r]], {n, 1, 150}] (* A329938 *)
Table[Floor[n*Cosh[r]], {n, 1, 150}] (* A329939 *)
CROSSREFS
Cf. A329825, A329831, A329937, A329939 (complement).
Sequence in context: A186328 A063460 A329831 * A247429 A187232 A187907
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, Jan 02 2020
STATUS
approved